What drives antigenic drift in a single influenza season
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What drives antigenic drift in a single influenza season?. Maciej F. Boni Stanford University, Department of Biological Sciences Co-authors: Julia R. Gog, Viggo Andreasen, Marcus W. Feldman. DIMACS Workshop on the Epidemiology and Evolution of Influenza Rutgers University, January 26, 2006.

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What drives antigenic drift in a single influenza season?

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What drives antigenic drift in a single influenza season

What drives antigenic drift in a single influenza season?

Maciej F. BoniStanford University, Department of Biological SciencesCo-authors: Julia R. Gog, Viggo Andreasen, Marcus W. Feldman

DIMACS Workshop on the Epidemiology and Evolution of Influenza

Rutgers University, January 26, 2006


Flu epidemics and antigenic drift

Strains have accumulated mutations. But how many?

epidemic strain

NOV

APR

Flu epidemics and antigenic drift

weekly illnesses/10,000 inhabitants (NL)

20

( focus will be on HA1 )

1996

1997

1998

de Jong et al (2000)


Ha1 polymorphism local datasets

HA1 polymorphism – local datasets

  • Coiras et al, Arch. Vir. (2001)

  • Schweiger et al, Med. Microbiol. Immunol. (2002)

  • Pyhälä et al, J. Med. Virol. (2004)

mean within-season distance = 2.8 aa (6nt)

max within-season distance = 8 aa (25nt)


Neutral epidemic model

Number of infections with epidemic-originating strain

Number of infections with a strain k mutations away

Neutral Epidemic Model


Neutral epidemic model1

Exiting a population class via mutation

Neutral Epidemic Model


Strain frequencies are poisson distributed

Strain frequencies are Poisson-distributed

Frequency of strain k:

Mean number of mutations per virus moves forward in time

according to a “molecular clock.”


Modeling antigenic drift and immunity

you may have conferred immunity from a previous season to one of these strains.

Modeling antigenic drift and immunity

the epidemic-originating strain

-2

-1

0

1

2

3

4


Modeling antigenic drift and immunity1

Modeling antigenic drift and immunity

the epidemic-originating strain

-2

-1

0

1

2

3

4

Distance between immunizing strain and challenging strain determines level of cross-immunity.

We model this as an infectivity reduction and say it wanes exponentially with distance:


Non neutral model

Non-neutral model

  • Amino-acid replacements in influenza surface proteins confer a fitness benefit via increased transmissibility

  • Hosts have some immunity structure from vaccination or previous infections

    ( need both )


Keeping track of hosts

j+kis distance between immunizing and challenging (infecting) strain

Keeping track of hosts


Keeping track of variables

infectivity reduction by previous infection

with a strain j amino acids away

force of infection of strain k

total force of infection

Keeping track of variables


Equations

Equations


Equations1

total immunity in population

cross-immunity between strains mamino acids apart

Equations


Equations2

mean fitness of strain population: W

Equations

fitness of strain k


Population genetics

Fisher’s Fundamental Theorem

Population genetics

Define mean antigenic drift in virus population as:

This is the Price Equation, thus, the basic influenza population dynamics

can be viewed in a standard population genetic framework.


Under neutrality

Under neutrality


What drives antigenic drift in a single influenza season

Takes 7 aa-changes to escape 50% immunity

I(t)


Define the excess antigenic drift as

Define the excess antigenic drift as:

How do you know when the epidemic ends?


What drives antigenic drift in a single influenza season

I(t)


In general how do the parameters affect the model results

In general, how do the parameters affect the model results?


Partial correlations

Partial correlations

immunity :

immune-escape/mutation :


Partial correlations1

Partial correlations

immunity :

immune-escape/mutation :


What drives antigenic drift in a single influenza season

Host immunity drives antigenic drift


Public health implications

Public health implications

  • Vaccination strategies: under-vaccination or imperfect vaccination may cause much excess antigenic drift.

  • Pandemic implications: need to consider the effects of vaccination during the 2nd year after a pandemic, and their effects on the 3rd year after a pandemic.


Thanks

Thanks

Viggo Andreasen

University of Roskile, Department of Mathematics and Physics

Julia Gog

Cambridge University, Department of Zoology

Marc Feldman

Stanford University, Department of Biological Sciences

Freddy Christiansen

University of Aarhus, Department of Biology

Mike Macpherson

Stanford University, Department of Biological Sciences

( and for funding to NIH grant GM28016, NSF, and Stanford University )


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